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A third-order class-D amplifier with and without ripple compensation

Cox, Stephen M.; du Toit Mouton, Hendrik

A third-order class-D amplifier with and without ripple compensation Thumbnail


Stephen M. Cox

Hendrik du Toit Mouton


We analyse the nonlinear behaviour of a third-order class-D amplifier, and demonstrate the remarkable effectiveness of the recently introduced ripple compensation (RC) technique in reducing the audio distortion of the device. The amplifier converts an input audio signal to a high-frequency train of rectangular pulses, whose widths are modulated according to the input signal (pulse-width modulation) and employs negative feedback. After determining the steady-state operating point for constant input and calculating its stability, we derive a small-signal model (SSM), which yields in closed form the transfer function relating (infinitesimal) input and output disturbances. This SSM shows how the RC technique is able to linearise the small-signal response of the device. We extend this SSM through a fully nonlinear perturbation calculation of the dynamics of the amplifier, based on the disparity in time scales between the pulse train and the audio signal. We obtain the nonlinear response of the amplifier to a general audio signal, avoiding the linearisation inherent in the SSM; we thereby more precisely quantify the reduction in distortion achieved through RC. Finally, simulations corroborate our theoretical predictions and illustrate the dramatic deterioration in performance that occurs when the amplifier is operated in an unstable regime. The perturbation calculation is rather general, and may be adapted to quantify the way in which other nonlinear negative-feedback pulse-modulated devices track a time-varying input signal that slowly modulates the system parameters.


Cox, S. M., & du Toit Mouton, H. (2018). A third-order class-D amplifier with and without ripple compensation. Physica D: Nonlinear Phenomena, 372,

Journal Article Type Article
Acceptance Date Jan 28, 2018
Online Publication Date Feb 3, 2018
Publication Date Jun 1, 2018
Deposit Date Feb 1, 2018
Publicly Available Date Feb 4, 2019
Journal Physica D: Nonlinear Phenomena
Print ISSN 0167-2789
Electronic ISSN 0167-2789
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 372
Keywords Class-D amplifier; pulse-modulated systems; PWM; piecewise-smooth systems
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